I also say don't do it. I shot a doe three years ago with my .38-40. It has a larger diameter bullet and twice the powder charge as the .32-20. After following the blood trail over 500 yards I lost it and could never find the deer. It probably eventually died or at least suffered from a long and painful wound. So if a .38-40 is too light for a deer, a .32-20 definitely is.

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(Luke 11:21 KJV) When a strong man armed keepeth his palace, his goods are in peace:

(Luke 22:36 KJV) Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.

In training for your hunt, you should practice walking downhill great distances, and retrieving 100# plus objects from the bottom of the hollow, and then back over the ridge you started on. Be sure not to detour around any thorny spots.

I'll trade 5# of "ruined meat" for a "great survivalist adventure" any day.

30-06 always makes an exit wound the size of a softball.
They bleed out fast if the shock of the bullet passing through-and-through doesn't just bowl them over right there.

I would choose something else unless you don't have a choice. If you don't, then take careful shots. I would choose a shotgun over the 32-20 and I don't particularly like deer hunting with a shotgun (slugs).

It sounds like you are planning on using it just because you "want to".

It may not have enough power where you hunt so you might want to check that out first. It will certainly work but as good as I am with a rifle I would hesitate a lot unless I was really desperate for that deer. Beats a 22 and it is way better than my old 25-20 which has a few deer to its credit by my old stepfathers grandfather but I won't use it if you can get another gun. Your old gun comes from the same era as mine did and we have learned a few things since then. Save it for coyotes and coon hunting.

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Good intentions will always be pleaded for any assumption of power. The Constitution was made to guard the people against the dangers of good intentions. There are men in all ages who mean to govern will, but they mean to govern. They promise to be good masters, but they mean to be masters.
--Daniel Webster--

The 32-20 I consider it an antiquated cartridge. But if the 32-20 is indeed legal to take a deer in your hunt area with? Your well within your Rights to use that (1889) Marlin of yours. I would advise: Place your first shot well and consider the necessity of a follow up shot without hesitation and perhaps more than two even may be required to harvest your deer with. Good Luck with your aspiration Sir.

Just because it is legal doesn't make it adequate. Here in Alabama the law just says rifle or pistol shooting a centerfire expanding bullet. That means my Ruger LCP .380 pistol is a legal deer gun. But would I ever try to kill a deer with it? No! I do carry a pistol during gun deer season but it is a Ruger Blackhawk in .45 Colt. I once passed up a six foot shot at a doe with the Blackhawk because I had seen a nice buck just a few minutes before and was hoping to get a shot at it. (I would have shot the buck with my .30-06!)

__________________
(Luke 11:21 KJV) When a strong man armed keepeth his palace, his goods are in peace:

(Luke 22:36 KJV) Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.

I popped a racoon in a leg trap right in the head with a ,32 and thought it was done, but after a while it woke up and required a couple more .22s to put paid to it.
Of course it waited until I got it home and dropped it in the yard to wake up. If it hadn't tanged the trap anchor chain, it probably could have got past the dogs and vamoosoed. If you must use a .32, the .32 Winchester Special is the ticket.

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